[When testing out new graph tools I like to see how it handles the graph of arccot(x). This is the one I found to be inconsistently graphed by Matlab, Mathematica, Mathcad and so on. Interestingly, Google doesn't even draw a graph for arccot(x)! See: Which is the correct graph of arccot(x)?]

3. Most popular IntMath Newsletter stories in 2011

I keep a fairly close eye on what my readers find most interesting. New subscribers would have missed some of these popular articles.

5. Math trends for 2012 (job opportunities in math)

Many of you will be joining the job market in the next few years. The world economy could be in for more shocks in 2012 and beyond, so it's important to keep on top of emerging trends. There will always be jobs for those who keep up with what's going on.

Trendwatching has some interesting ideas on what will impact commerce - and therefore jobs - next year. For those with math skills, several of these trends will provide opportunities.

DIY Health This is all about data gathering and intepretation - and ethics and privacy.

ECOCYCOLOGY Engineers will need to work on efficiencies and optimization in order to make compulsory recycling commercially viable.

6. IntMath Poll: Calculators in math class

The recent IntMath Poll asked readers Which calculator do you use during math lessons?

The "no calculator" choice could be for 3 reasons - either most students don't have a calculator in a particular class, or maybe the math teacher doesn't approve of calculators, or finally, students use computers instead.

TI-83, 84 or 89 39%

Casio FX 35%

No calculator 11%

Other calculator 9%

TI-NSpire 6%

Total responses: 4000.

Latest poll: How social is your math? The current poll asks readers if they study for math tests alone, or with a group of friends. The results so far are interesting. You can vote on any page on IntMath.com.

7. Friday math movie: U + Me = Us (calculus)

Here's a fun video from boy band 2gether, with mathematical mentions. This is a light one to finish the year!

8. Final thought: No regrets

The end of each year is a chance to reflect on what we have achieved and to plan for the coming year. This quote by Sydney J. Harris, Chicago-based journalist, may help give some perspective.

Regret for things we did can be tempered by time; it is regret for the things we did not do that is inconsolable. [Sydney J. Harris]

Those who aim to live up to their potential enjoy their lives the most. And that goes for math, too!

9. Season's Greetings and coming up

Here's wishing everyone a safe and enjoyable Christmas, Hanukkah, New Year, Lohri (mid-January), Mawlid an-Nabi (in early February) and whatever other holiday or cultural event you celebrate at this time of the year.

I'm hoping 2012 will treat you well. Work smart, and watch the trends!

There'll be several changes to the IntMath Newsletter next year, new features on IntMath and many new articles on the blog - watch this space for details.